Wavelet transforms: Application to data analysis - II

Resonance ◽  
2004 ◽  
Vol 9 (12) ◽  
pp. 8-13 ◽  
Author(s):  
Jatan K. Modi ◽  
Sachin P. Nanavati ◽  
Amit S. Phadke ◽  
Prasanta K. Panigrahi
Keyword(s):  
Data Analysis ◽  
Wavelet Transforms

Wavelet transforms: Application to data analysis - I

Resonance ◽  
2004 ◽  
Vol 9 (11) ◽  
pp. 10-22 ◽  
Author(s):  
Jatan K. Modi ◽  
Sachin P. Nanavati ◽  
Amit S. Phadke ◽  
Prasanta K. Panigrahi
Keyword(s):  
Data Analysis ◽  
Wavelet Transforms

Gravity and magnetic data analysis based on Poisson wavelet-transforms

2020 ◽  
Author(s):  
Kirill Kuznetsov ◽  
Bulychev Andrey ◽  
Ivan Lygin
Keyword(s):  
Data Analysis ◽  
Magnetic Fields ◽  
Potential Field ◽  
Wavelet Transforms ◽  
Geophysical Methods ◽  
Magnetic Data ◽  
Potential Field Data ◽  
Gravity And Magnetic ◽  
Gravity And Magnetic Data ◽  
Poisson Wavelets

<p>Studies of the Earth’s interior structure are one of the most complex topics in modern science. Integration of different geophysical methods plays a key role in effectively tackling the problem. In the last decade capabilities of potential field geophysical methods have been increasing due to development of advanced digital technologies. Improved resolution and accuracy of gravity and magnetic fields measurements made by modern equipment makes it possible to build more detailed geological models. Different tectonic and structural elements being interpreted in such models produce potential field signals with different spectral characteristics. Like any geophysical signals, potential fields can be described as a spatially non-stationary signal. This means its frequency content may change depending on a given signal sample, in particular with different spatial location of a sample. In this case, approaches of gravity and magnetic fields analysis based on Fourier transform or signal decomposition into a number of harmonic functions can lead to incorrect results. One of the ways to solve this challenge involves using wavelet transform based algorithms, since these transforms do not assume stationary signals and each function of a wavelet-based basis is localized in space domain.</p><p>In gravity and magnetic data analysis it is beneficial to use wavelets based on partial derivatives of the Poisson kernel, which correspond to derivatives of a point source gravity potential. Application of Poisson wavelets in potential field data analysis has begun in the 1990's and is predominantly aimed at studying gravity and magnetic fields singularity points during data interpretation.</p><p>Similar to Fourier-based potential field techniques, it is possible to construct a number of data filtering algorithms based on Poisson wavelets. Current work demonstrates that it is possible to construct algorithms based on Poisson wavelets for transforming profile and spatially gridded gravity and magnetic data, e.g. for calculation of equivalent density and magnetization distributions, upward and downward continuations, reduction to pole and many other filters that take into account spatial distribution of the signal.</p><p>Wavelet-transforms allow to account for spatially non-stationary nature of geophysical signals. Use of wavelet based techniques allows to effectively carry out potential field data interpretation in a variety of different geologic and tectonic settings in a consistent fashion.</p>

Application of Wavelet Transforms to Reservoir-Data Analysis and Scaling

SPE Journal ◽  
2000 ◽  
Vol 5 (01) ◽  
pp. 92-101 ◽  
Author(s):  
M.N. Panda ◽  
C.C. Mosher ◽  
A.K. Chopra
Keyword(s):  
Data Analysis ◽  
Wavelet Transforms

Fatigue Data Analysis Using Continuous Wavelet Transform and Discrete Wavelet Transform

2011 ◽  
Vol 462-463 ◽  
pp. 461-466 ◽  
Author(s):  
Shahrum Abdullah ◽  
S.N. Sahadan ◽  
Mohd Zaki Nuawi ◽  
Zulkifli Mohd Nopiah
Keyword(s):  
Wavelet Transform ◽  
Data Analysis ◽  
Discrete Wavelet Transform ◽  
Wavelet Transforms ◽  
Data Extraction ◽  
Morlet Wavelet ◽  
Analysis Time ◽  
Discrete Wavelet ◽  
Continuous Wavelet ◽  
Fatigue Data

The wavelet transform is well known for its ability in vibration analysis in fault detection. This paper presents the ability of wavelet transform in fatigue data analysis starts from high amplitude events detection and it is then followed by fatigue data extraction based on wavelet coefficients. Since the wavelet transform has two main categories, i.e. the continuous wavelet transforms (CWT) and the discrete wavelet transform (DWT), the comparison study were carried out in order to investigate performance of both wavelet for fatigue data analysis. CWT represents by the Morlet wavelet while DWT with the form of the 4th Order Daubechies wavelet (Db4) was also used for the analysis. An analysis begins with coefficients plot using the time-scale representation that associated to energy coefficients plot for the input value in fatigue data extraction. Ten extraction levels were used and all levels gave the damage difference, (%∆D) less than 10% with respect to original signal. From the study, both wavelet transforms gave almost similar ability in editing fatigue data but the Morlet wavelet provided faster analysis time compared to the Db4 wavelet. In comparison to have the value of different at 5%, the Morlet wavelet achieved at L= 5 while the Db4 wavelet at L=7. Even though it gave slower analysis time, both wavelets can be used in fatigue data editing but at different time consuming.

Geophysical data analysis with wavelet transforms

1998 ◽  
Author(s):  
Douglas J. Foster ◽  
Charles C. Mosher ◽  
F. D. Lane
Keyword(s):  
Data Analysis ◽  
Wavelet Transforms ◽  
Geophysical Data

Application of Wavelet Transforms to Reservoir Data Analysis and Scaling

1996 ◽  
Author(s):  
M.N. Panda ◽  
C. Mosher ◽  
A.K. Chopra
Keyword(s):  
Data Analysis ◽  
Wavelet Transforms

scholarly journals WAVELET TRANSFORMS FOR THE STATISTICAL ANALYSIS OF RETURNS GENERATING STOCHASTIC PROCESSES

2001 ◽  
Vol 04 (03) ◽  
pp. 511-534 ◽  
Author(s):  
ENRICO CAPOBIANCO
Keyword(s):  
Data Analysis ◽  
Statistical Analysis ◽  
Stochastic Processes ◽  
High Frequency ◽  
Wavelet Transforms ◽  
Exploratory Data Analysis ◽  
Statistical Procedure ◽  
Stock Index ◽  
Garch Models ◽  
Exploratory Data

We study high frequency Nikkei stock index series and investigate what certain wavelet transforms suggest in terms of volatility features underlying the observed returns process. Several wavelet transforms are applied for exploratory data analysis. One of the scopes is to use wavelets as a pre-processing smoothing tool so to de-noise the data; we believe that this procedure may help in identifying, estimating and predicting the latent volatility. Evidence is shown on how a non-parametric statistical procedure such as wavelets may be useful for improving the generalization power of GARCH models when applied to de-noised returns.

Paper machine data analysis and display using wavelet transforms

2002 ◽  
Author(s):  
S. McLeod ◽  
Z. Nesic ◽  
M.S. Davies ◽  
G.A. Dumont ◽  
F. Lee ◽  
...  
Keyword(s):  
Data Analysis ◽  
Wavelet Transforms ◽  
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